# Properties

 Label 3344.2.o.b Level $3344$ Weight $2$ Character orbit 3344.o Analytic conductor $26.702$ Analytic rank $0$ Dimension $64$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$3344 = 2^{4} \cdot 11 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3344.o (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$26.7019744359$$ Analytic rank: $$0$$ Dimension: $$64$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## $q$-expansion

The dimension is sufficiently large that we do not compute an algebraic $$q$$-expansion, but we have computed the trace expansion.

 $$\operatorname{Tr}(f)(q) =$$ $$64 q + 56 q^{9}+O(q^{10})$$ 64 * q + 56 * q^9 $$\operatorname{Tr}(f)(q) =$$ $$64 q + 56 q^{9} + 16 q^{17} + 64 q^{25} + 32 q^{45} - 88 q^{49} + 32 q^{57} + 64 q^{61} + 40 q^{73} - 48 q^{81} - 24 q^{85} + 80 q^{93}+O(q^{100})$$ 64 * q + 56 * q^9 + 16 * q^17 + 64 * q^25 + 32 * q^45 - 88 * q^49 + 32 * q^57 + 64 * q^61 + 40 * q^73 - 48 * q^81 - 24 * q^85 + 80 * q^93

## Embeddings

For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below.

For more information on an embedded modular form you can click on its label.

Label $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
1519.1 0 −3.22672 0 −2.25376 0 1.49199i 0 7.41170 0
1519.2 0 −3.22672 0 −2.25376 0 1.49199i 0 7.41170 0
1519.3 0 −3.09364 0 1.45449 0 2.09473i 0 6.57062 0
1519.4 0 −3.09364 0 1.45449 0 2.09473i 0 6.57062 0
1519.5 0 −2.58608 0 3.42833 0 4.59904i 0 3.68782 0
1519.6 0 −2.58608 0 3.42833 0 4.59904i 0 3.68782 0
1519.7 0 −2.58114 0 4.01759 0 1.30410i 0 3.66230 0
1519.8 0 −2.58114 0 4.01759 0 1.30410i 0 3.66230 0
1519.9 0 −2.50544 0 −2.98570 0 4.82712i 0 3.27725 0
1519.10 0 −2.50544 0 −2.98570 0 4.82712i 0 3.27725 0
1519.11 0 −2.16100 0 −1.12654 0 1.31746i 0 1.66990 0
1519.12 0 −2.16100 0 −1.12654 0 1.31746i 0 1.66990 0
1519.13 0 −2.07682 0 −4.09903 0 1.91903i 0 1.31320 0
1519.14 0 −2.07682 0 −4.09903 0 1.91903i 0 1.31320 0
1519.15 0 −2.05926 0 1.15495 0 3.33583i 0 1.24056 0
1519.16 0 −2.05926 0 1.15495 0 3.33583i 0 1.24056 0
1519.17 0 −1.53236 0 −0.205404 0 1.77369i 0 −0.651867 0
1519.18 0 −1.53236 0 −0.205404 0 1.77369i 0 −0.651867 0
1519.19 0 −1.41745 0 2.36069 0 2.85642i 0 −0.990838 0
1519.20 0 −1.41745 0 2.36069 0 2.85642i 0 −0.990838 0
See all 64 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 1519.64 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
4.b odd 2 1 inner
19.b odd 2 1 inner
76.d even 2 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 3344.2.o.b 64
4.b odd 2 1 inner 3344.2.o.b 64
19.b odd 2 1 inner 3344.2.o.b 64
76.d even 2 1 inner 3344.2.o.b 64

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
3344.2.o.b 64 1.a even 1 1 trivial
3344.2.o.b 64 4.b odd 2 1 inner
3344.2.o.b 64 19.b odd 2 1 inner
3344.2.o.b 64 76.d even 2 1 inner